Method of locating a source of pulses in a dispersive medium

ABSTRACT

The invention relates to a method of locating in a dispersive medium ( 5 ) a source ( 7 ) of pulses (s 1 , s 2 ) by at least one pair of sensors ( 1, 2 ), the method comprising the following steps: at the level of each sensor ( 1, 2 ), detecting a pulse (s 1 , s 2 ) originating from the source ( 7 ); for each of said pulses, constructing a phase diagram on the basis of N vectors of which the co-ordinates correspond to the amplitude of the pulse (s 1 , s 2 ) at successive sampling instants t i ; and for each pair of sensors, calculating the ratio between the distances L 1  and L 2  of each sensor from the source through the formula (I) where (II) and (III) are the norms of the vectors (IV) and (V) of the phase diagrams corresponding to the pulses detected by the sensors ( 1, 2 ). 
     
       
         
           
             
               
                 
                   
                     
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CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a National Stage of PCT International Application Serial Number PCT/EP2015/050106, filed Jan. 6, 2015, claims priority under 35 U.S.C. §119 of France, patent application Ser. No. 14/50348, filed Jan. 16, 2014, the disclosures of which are incorporated by reference herein.

BACKGROUND

The present disclosure relates to a method for locating a pulse source in a dispersive medium.

DISCUSSION OF RELATED ART

In carrier lines, for example, for electric energy, water, or data, different phenomena may result in the generation of pulses at one point of the lines. It is then desired to detect and to locate the area from which the pulses originate.

As an example, in an electric cable, a defect in the cable isolation may result in the occurrence of parasitic electric discharges, each discharge causing the generation of a pulse having a duration, or width, generally shorter than 1 μs.

Locating the pulse source enables to locate the defect and thus to replace or to repair the cable section affected by the defect. An error as to the exact position of the pulse source may result in taking action on a wrong cable portion and in having to repeat the maintenance operation.

FIG. 1 schematically shows a device capable of locating a pulse source on a line.

Two sensors 1 and 2 are arranged on an electric cable 5, on either side of an electric pulse source 7. Each sensor is associated with communication means (not shown) and with a signal processing unit (not shown).

A known cable length, L separates sensor 1 from sensor 2. The cable lengths, L1 and L2, separating source 7 respectively from sensor 1 and from sensor 2, are desired to be known.

When an electric discharge 10 occurs at the level of source 7, pulses s1 and s2 propagate all the way to sensors 1 and 2. In the shown example, length L1 being greater than length L2, pulse s1 is received by sensor 1 a time At after pulse s2 has been received by sensor 2. Interval At is inversely proportional to the pulse propagation speed in the cable and proportional to the difference between lengths L1 and L2. By measuring At, knowing the speed and the length of cable L between the sensors, L1 or L2, and thus the position of source 7 on cable 5, are calculated.

To measure At, sensors 1 and 2 should be synchronized by means of systems such as GPS (“Global Positioning System”) modules, radio modems, or optical fiber. A synchronization delay between sensors 1 and 2 causes an error on At and thus on the exact position of source 7. As an example, for a propagation speed v=1.6*108 m.s−1, a 160-ns error on the value of Δt causes an error on the source position equal to 25.6 m.

Documents “IEEE TRANSACTIONS ON POWER DELIVERY, IEEE SERVICE CENTER, NEW-YORK, N.Y., US, vol. 26, no. 1, Jan. 1, 2011, pages 33-41” DE 10 2010 013613, WO 2005/073752, and “INFORMATION SCIENCE, SIGNAL PROCESSING AND THEIR APPLICATIONS (ISSPA), 2012 11TH INTERNATIONAL CONFERENCE ON, IEEE, Jul, 2, 2012, pages 1141-1146” describe various defect location systems.

SUMMARY

The error in terms of source location is here desired to be decreased.

Thus, an embodiment provides a method of locating in a dispersive medium a pulse source by means of at least one pair of sensors, the method comprising the steps of: at the level of each sensor, detecting a pulse originating from the source; for each of said pulses, constructing a phase diagram from N vectors having their coordinates corresponding to the pulse amplitude at successive sampling times t_(i); and for each pair of sensors, calculating the ratio between distances L₁ and L₂ of each sensor to the source by formula:

L ₁ /L ₂=Σ_(i=1) ^(N)|{right arrow over (r ₁(t _(i)))}|/Σ_(i−1) ^(N)|{right arrow over (r ₂(t _(i)))}|

when |{right arrow over (r₁(t_(i)))}| and |{right arrow over (r₂(t_(i)))}| are the norms of vectors {right arrow over (r₁(t_(i)))} and {right arrow over (r₂(t_(i)))} of the phase diagrams corresponding to the pulses detected by the sensors.

According to an embodiment, the dispersive medium is a guided medium.

According to an embodiment, the source is located by a pair of sensors, distance L between the sensors being known.

According to an embodiment, the dispersive medium is an electric cable.

According to an embodiment, the coordinates of the vectors of the phase diagrams correspond to three successive sampling times.

According to an embodiment, the detection of a pulse at the level of each sensor comprises the steps of: splitting a signal received by the sensor into portions of same duration; filtering each portion with a plurality M of bandpass filters having different central frequencies f_(j); calculating an average energy level associated with each frequency f_(j) of a portion; calculating a spectral distance D_(W/W+1) between first and second successive portions; and comparing spectral distance D_(W/W+1) with a threshold.

According to an embodiment, the threshold value is set during a previous calibration step.

According to an embodiment, spectral distance D_(W/W+1) is calculated based on the following formula:

$D_{{W/W} + 1} = \sqrt{\left( {\sqrt{\sum_{i = 1}^{M}\left( {X^{W + 1}\left( f_{j} \right)} \right)^{2}} - \sqrt{\sum_{i = 1}^{M}\left( {X^{W}\left( f_{j} \right)} \right)^{2}}} \right)}$

where X^(W) (f_(i)) and K^(W+1)(f_(i)) are the average energy levels corresponding to frequency f_(j) respectively of the first portion and of the second portion.

According to an embodiment, the duration of a portion is in the range from 5 to 15 μs.

According to an embodiment, the pitch separating two successive sampling times is in the range from 1 to 50 ns.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings, among which:

FIG. 1, previously described, schematically shows a device capable of locating a source of electric pulses on a cable;

FIG. 2 schematically shows an embodiment of a device for locating a source of electric pulses on a cable;

FIG. 3 shows the shape of pulses detected at the level of the sensors of FIG. 2;

FIG. 4 illustrates a mode of pulse detection by the device of FIG. 2;

FIGS. 5A and 5B respectively show a pulse and a phase diagram corresponding to this pulse; and

FIGS. 6A and 6B respectively are phase diagrams of two pulses and a projection on a plane of the diagrams.

For clarity, the same elements have been designated with the same reference numerals in the different drawings.

DETAILED DESCRIPTION

The embodiments described in detail hereafter aim at locating a source of electric pulses corresponding to electric discharges at one point of an electric cable. More generally, the method applies to the locating of any type of pulse source in any type of dispersive medium, be it guided or not. Another example of a guided dispersive medium is a water pipe. In this case, the pulses to be detected are not electric pulses but overpressure pulses. In the case of a non-guided dispersive medium, three sensors at least are used and the position of the pulse source is determined by triangulation based on the ratios between the distances from the source to each of the sensors. An example of a non-guided dispersive medium is a stressed mechanical part where internal breakage areas are desired to be located, the sensors then being vibration sensors or sound sensors.

FIG. 2 schematically illustrates an embodiment of a device for detecting a source of electric pulses in an electric cable.

The device comprises two sensors, 1 and 2, arranged at a distance L from each other on an electric cable 5, on either side of a source of electric pulses 7. Each sensor is associated with a signal processing unit 12 and with communication means 14. The device further comprises a calculation unit 16 associated with communication means 14. Calculation unit 16 receives data from the sensor. Communication means 14 may be wired or wireless means, for example, an optical fiber or powerline communication connection.

The cable lengths L₁ and L₂ separating source 7 from sensors 1 and 2 are desired to be known. When an electric discharge 10 occurs at the level of source 7, pulses s₁ and s₂, initially identical, respectively propagate towards sensor 1 and towards sensor 2.

FIG. 3 shows the shape of pulses s₁ and s₂ placed opposite each other. Pulse s₁ is more attenuated and more deformed than pulse s₂. This is the consequence of the fact that propagation distance L₁ of pulse s₁ is greater than propagation distance L₂ of pulse s₂ and of the fact that cable 5 is a dispersive medium.

It is here provided to determine distance L₁ and L₂ from the shape difference of pulses s₁ and s₂ rather than from the propagation time difference between these pulses. Thus, it is not necessary to synchronize sensors 1 and 2 of FIG. 2 together. It is thus not necessary to associate with these sensors expensive or sophisticated synchronization means as described in relation with FIG. 1.

The inventor has shown that the ratio between lengths L₁ and L₂ is equal to the ratio of the sum of the norms of the vectors of a phase diagram of pulse s₁ to the sum of the norms of the vectors of a phase diagram of pulse s₂.

It is here provided to detect pulses s₁ and s₂ and then to reconstruct their phase diagram and to calculate the above-mentioned ratio.

FIG. 4 schematically illustrates an example of a transient signal detection method.

At a step 20, a signal 22 received by sensors 1 or 2 is split into portions ( . . . W, W+1, W+2, . . . ) of same duration. As an example, to detect a pulse having a width smaller than or equal to 1 μs, the duration of a portion is in the range from 5 to 25 μs, for example, 15 μs.

At a step 26, a filtering is applied to each portion W by an assembly of M bandpass filters, each having a different central frequency f_(j), j being in the range from 1 to M.

At a step 28, an average level X^(W)(f_(j)) is calculated for each frequency f_(j) of each portion W. This average energy level may be obtained by associating an integrator circuit with each of the M filters.

At a step 30, for any pair of successive portions W and W+1, a spectral distance D_(W/W+1) is calculated based on the following formula:

$D_{{W/W} + 1} = \sqrt{\left( {\sqrt{\sum_{i = 1}^{M}\left( {X^{W + 1}\left( f_{j} \right)} \right)^{2}} - \sqrt{\sum_{i = 1}^{M}\left( {X^{W}\left( f_{j} \right)} \right)^{2}}} \right)}$

At a step 32, spectral distance D_(W/W+1) is compared with a threshold β set in a previous calibration phase. One can deduce from the fact that D_(W/W+1) becomes greater than β that portion W+1 contains a signal other than noise (a pulse).

FIGS. 5A and 5B illustrate the construction of a phase diagram (shown in FIG. 5B) from the amplitude of a pulse (shown in FIG. 5A). The construction of a phase diagram from a signal is disclosed at chapter 3, pages 30 to 46, of the second edition of book “Non-linear Time Series Analysis” by Holger Kantz and Thomas Schrieber published in 2004 by Cambridge University Press.

FIG. 5A shows the amplitude A of a pulse 39 versus time t. Pulse 39 is regularly sampled with a pitch ti at successive times t_(i) having amplitudes a(t_(i)) corresponding thereto.

FIG. 5B shows an orthonormal coordinate system 40 with axes X, Y, and Z. Referring to FIG. 5A, a vector {right arrow over (r(t_(i)))} may be associated with each sampling time t_(i) such that the coordinates of vector {right arrow over (r(t_(i)))} along the three axes X, Y, and Z correspond to a(t_(i)), a(t_(i)+τ), and a(t_(i)+2τ) that is, to the amplitudes of pulse 39 at sampling times t_(i), t_(i)+τ, and t_(i)+2τ. The set of vectors {right arrow over (r(t_(i)))} forms, in coordinate system 40, phase diagram 42 of pulse 39. As an example, to determine a phase diagram of a pulse having a width smaller than or equal to 1 μs, sampling pulse τ is in the range from 1 to 50 ns, for example, 20 ns (that is, a 50-MHz sampling frequency).

In the described example, vectors {right arrow over (r(t_(i)))} have three dimensions. Generally, vectors {right arrow over (r(t_(i)))} may be associated with a number D of sampling times in a D-dimensional coordinate system, D≧2.

FIG. 6A shows two phase diagrams 44 and 46 respectively associated with pulses s₁ and s₂. Phase diagram 44 is formed of the N vectors {right arrow over (r₁(t_(i)))} determined from pulse s₁. Phase diagram 46 is formed of the N vectors {right arrow over (r₂(t_(i)))} determined from pulse s₂. Phase diagram 46 is substantially an enlargement of phase diagram 44.

In FIG. 6B, phase diagrams 44 and 46 have been projected on plane XY of FIG. 6A to better highlight the fact that phase diagram 46 is substantially an enlargement of phase diagram 44.

As previously indicated, the ratio between distances L₁ and L₂ is equal to the ratio of the sum of the norms of the vectors of a phase diagram of pulse s₁ to the sum of the norms of the vectors of a phase diagram of pulse s₂. In other words:

L ₁ /L ₂=Σ_(i=1) ^(N)|{right arrow over (r ₁(t _(i)))}|/Σ_(i=1) ^(N)|{right arrow over (r ₂(t _(i)))}|

where |{right arrow over (r₁(t_(i)))}| and |{right arrow over (r₂(t_(i)))}| are the norms of vectors {right arrow over (r₁(t_(i)))} and {right arrow over (r₂(t_(i)))}.

Laboratory tests have been carried out by the inventor and show that such a method enables to locate a pulse source with a better accuracy than in the case of a method based on differences of times of arrival of pulses at the level of sensors. As an example, when sensors are arranged on a coaxial cable, 300 m away from each other, the position of a pulse source is determined with an error of 1.024 m only, and not 25.6 m as in the case of FIG. 1.

Specific embodiments have been described. Various alterations and modifications will occur to those skilled in the art. In particular, although an embodiment has been described in the case of electric pulses propagating in an electric cable, it should be reminded that the method applies to any type of dispersive medium, be it guided or not, and to different natures of signals. In the case of a non-guided dispersive medium, the phase diagrams of pulses detected at the level of at least three sensors enable to calculate ratios between the distances from the source to each of the pails of sensors. The exact position of the source can then be deduced from such ratios by triangulation.

Further, the method has been described in the case where sensors are located on either side of a pulse source. They may also be arranged on the same side of a source. 

1. A method of locating in a dispersive medium a source of pulses with at least a pair of sensors, the method comprising the steps of: detecting a pulse at the level of each sensor originating from the source; constructing a phase diagram for each of said pulses from N vectors having their coordinates corresponding to the amplitude of the pulse at a sampling time ti and at next successive sampling times; and calculating the ratio for each pair of sensors between distances L1 and L2 from each sensor to the source with formula: L ₁ /L ₂Σ_(i=1) ^(N)|{right arrow over (r ₁(t _(i)))}|/Σ_(i=1) ^(N)|{right arrow over (r ₂(t _(i)))}| where |{right arrow over (r₁(t_(i)))}|and |{right arrow over (r₂(t_(i)))}| are the norms of vectors {right arrow over (r₁(t_(i)))} and {right arrow over (r₂(t_(i)))} of the phase diagrams corresponding to the pulses detected by the sensors.
 2. The method of claim 1, wherein the dispersive medium is a guided medium.
 3. The method of claim 2, wherein the source is located by a pair of sensors, distance L between sensors being known.
 4. The method of claim 2, wherein the dispersive medium is an electric cable.
 5. The method of claim 1, wherein the coordinates of the vectors of the phase diagrams correspond to three successive sampling times.
 6. The method of claim 1, wherein the detection of a pulse at the level of each sensor comprises the steps of: dividing a signal received by the sensor into portions of same duration; filtering each portion with a plurality M of bandpass filters having different central frequencies fj; calculating an average energy level associated with each frequency fj of a portion; calculating a spectral distance DW/W+1 between a first and a second successive portions; and comparing spectral distance DW/W+1 with a threshold.
 7. The method of claim 6, wherein the value of the threshold is set during a previous sampling state.
 8. The method of claim 6, wherein spectral distance DW/W+1 is calculated based on the following formula: D _(W/W+1)=√{square root over ((√{square root over (Σ_(i=1) ^(M)(X ^(W+1)(f _(j)))²)}−√{square root over (Σ_(i=1) ^(M)(X ^(W)(f _(j)))²)})² )} where X^(W)(f_(j)) and X^(W+1)(f_(j)) are the average energy levels corresponding to frequency fj respectively of the first portion and of the second portion.
 9. The method of claim 6, wherein the duration of a portion is in the range from 5 to 15 μs.
 10. The method of claim 1, wherein each step separating two successive sampling times is in the range from 1 to 50 ns.
 11. The method of claim 1, wherein the source is located by a pair of sensors, distance L between sensors being known.
 12. The method of claim 3, wherein the coordinates of the vectors of the phase diagrams correspond to three successive sampling times.
 13. The method of claim 4, wherein the coordinates of the vectors of the phase diagrams correspond to three successive sampling times.
 14. The method of claim 3, wherein the detection of a pulse at the level of each sensor comprises the steps of: dividing a signal received by the sensor into portions of same duration; filtering each portion with a plurality M of bandpass filters having different central frequencies fj; calculating an average energy level associated with each frequency fj of a portion; calculating a spectral distance DW/W+1 between a first and a second successive portions; and comparing spectral distance DW/W+1 with a threshold.
 15. The method of claim 4, wherein the detection of a pulse at the level of each sensor comprises the steps of: dividing a signal received by the sensor into portions of same duration; filtering each portion with a plurality M of bandpass filters having different central frequencies fj; calculating an average energy level associated with each frequency fj of a portion; calculating a spectral distance DW/W+1 between a first and a second successive portions; and comparing spectral distance DW/W+1 with a threshold.
 16. The method of claim 5, wherein the detection of a pulse at the level of each sensor comprises the steps of: dividing a signal received by the sensor into portions of same duration; filtering each portion with a plurality M of bandpass filters having different central frequencies fj; calculating an average energy level associated with each frequency fj of a portion; calculating a spectral distance DW/W+1 between a first and a second successive portions; and comparing spectral distance DW/W+1 with a threshold.
 17. The method of claim 14, wherein the value of the threshold is set during a previous sampling state.
 18. The method of claim 15, wherein the value of the threshold is set during a previous sampling state.
 19. The method of claim 16, wherein the value of the threshold is set during a previous sampling state.
 20. The method of claim 7, wherein spectral distance DW/W+1 is calculated based on the following formula: D _(W/W+1)=√{square root over ((√{square root over (Σ_(i=1) ^(M)(X ^(W+1)(f _(j)))²)}−√{square root over (Σ_(i=1) ^(M)(X ^(W)(f _(j)))²)})² )} where X^(W)(f_(j)) and X^(W+1)(f_(j)) are the average energy levels corresponding to frequency fj respectively of the first portion and of the second portion. 